There is a physical component to every emotion, and an emotional component to every physical sensation. Building a barrier between the two can help you control both.
For instance, something may make you sad. That sadness will, in turn, have a variety of physical effects on you – your eyes might water. You might lose energy. Your chest might hurt. You might have difficulty breathing. All of those things suck. But the thing that’s making you sad isn’t causing those things directly, unless the thing making you sad is the fact that you just got hit with some tear gas.
So when something makes you sad, acknowledge it. Recognize that there is an external force of some kind, and it is attempting to solicit an emotional reaction from you. The physical reaction you have is a perfectly rational response, from your body’s standpoint; the goal of your body is to make being sad unpleasant for you, so that you’ll avoid the things that make you sad, because from your programmed-by-survival-instincts body’s point of view, “things that make you sad” is more or less equivalent to “things that might kill you.” Your body’s just looking out for you, man.
So acknowledge it. Say to yourself, “okay, I get it. This is a thing I should avoid. I’ll do that. No need to give me the waterworks, too. Good looking out.” Recognize, and insulate.
You can do the same thing the other way. If you stub your toe, you might get angry. That shit hurts. If you’re already prone to anger, that’ll definitely do it. So instead, insulate. Acknowledge it. “There are a bunch of stimulated nerves sending signals to my brain alerting me to danger. The ‘red alert’ response is because my body has to treat any source of pain as a potential threat to my existence, and anger can give me the strength and speed to fight that threat off. But this isn’t a lion; it’s a coffee table. It’s cool. Thanks for the head’s up, though, good to know you’ve got my back.”
This can take some practice, but it’s marvelous once you get the hang of it. Once you recognize that every physical and emotional sensation you “feel” is just specific sets of chemicals released in response to specific stimuli, you can watch them happen, ride the wave out, and control what happens to you as a result. There are virtually zero situations in the modern world where you’re actually better off as a result of the behavioral influence from negative physical/emotional sensations, so learning to insulate yourself from those influences will help you keep control of your rudder in the storm.